The movie could have been called Stern's List, but that doesn't have the same ring to it. Still, this guy is the one maintaining the list and sneaking people onto it.
Stern's the accountant and general manager in Schindler's factory. He's also the closest thing Oskar has to a real friend, even though they start out in a decidedly less-than-friendly relationship. Stern works for the Judenrat: the governing body of the Jewish ghetto in Warsaw, charged with enforcing the will of the ruling Germans. Schindler comes to him recruiting for his factory. Stern doesn't like the deal. Why not? Because Schindler isn't planning to pay anyone.
STERN: Let me understand. They put up all the money. I do all the work. What, if you don't mind my asking, would you do?
Stern's not happy about the answer, which is basically that Oskar's going to exploit Jewish labor. But he doesn't have many cards to play, and he's going to play what he has as well as he can. He needs Schindler but doesn't warm up to him; he's suspicious of Oskar's opportunism.
Right away, we can see Stern's compassion for his fellow Jews. Having secured his position with Oskar, he quietly begins finding ways to get at-risk people to work in the factory, where they'll be temporarily safe and can use cooking pots to trade for frivolous luxuries like food. He's willing to use what little power he has for the sake of the most vulnerable in his community.
That makes him the perfect foil for Schindler, whose moral compass is in serious need of recalibration. Sure, Schindler's using the Jews, but with Stern's help, maybe the Jews can use him a little, too. Turns out, it works surprisingly well. The Jews stay out of harm's way—at least as close as any of them can hope for—and Schindler gets the immensely profitable factory he dreamed about as a kid.
Schindler's actually grateful for it, to the point of pulling Stern off of a train bound for a concentration camp rather than just replacing him with another accountant. He claims he's doing it for selfish reasons ("What if I got here five minutes later? Then where would I be?"), but it's soon clear that he sees his manager as something more than just an asset to be exploited.
Like all great bromances, we don't see it in words. Because he's close to Schindler, he can provide quiet moral guidance to keep his boss's eyes open. He types up the list of life for Schindler, scarcely believing that the man spent a literal steamer trunk full of money on bribes to make it happen. In the end, when he sees what Schindler accomplished, he's the first to step forward and touch the man's shoulder as his moral equal. "Whoever saves one life saves the world entire," he tells Oskar.
SCHINDLER: If I'd made more money...I threw away so much money, you have no idea. If I'd just...
STERN: There will be generations because of what you did.
SCHINDLER: I didn't do enough.
STERN: You did so much.
Maybe Stern saw a lot of himself in Oskar. Both were able to to see an opportunity when it presented itself. Stern's motivations weren't mercenary, but he was as smart as Oskar, maybe smarter, in exploiting loopholes and getting around restrictions. Especially considering the conditions Stern was working under—the constant threat of exposure and death—he showed enormous courage in trying to skirt the rules.
The real-life Stern was born in Austria, and served as a great source of first-hand knowledge about the kind of man Oskar Schindler was. He testified to it in Israel at a meeting of Schindler and the Jews he saved. He died in 1969, but his widow was one of the people portrayed at the end of the film visiting Schindler's gravesite.